6. In triangle ABC, angle B is equal to angle C, the point D falls 6. on BC, and angle BAD is equal to angle CAD. Prove that BD is6. equal to DC, and that AD is perpendicular to BC.

(Prove that triangles ADB, ADC are congruent.)

Since angle B is equal to angle C, then the sides opposite them, the sides AB, AC, are equal.
And since, by hypothesis, angle BAD is equal to angle CAD,
and side AD is common to the triangles ADB, ADC,
the remaining side BD is equal to the remaining side DC. (S.A.S.)
Further, angle ADB, opposite side AB, is equal to the adjacent angle ADC, opposite the equal side AC.
Therefore AD is perpendicular to BC. (Definition 3.)